Answer
$$z=3 \left ( \cos \pi +i \sin \pi \right )$$
Work Step by Step
We plot the complex number $z=-3$ the same way we plot $(-3,0)$ in the rectangular coordinate system.
Please note that the complex number $z=a+bi$ is written in polar form as$$z=r(\cos \theta +i \sin \theta ),$$where $a=r\cos \theta$, $b=r\sin \theta$, $r=\sqrt{a^2+b^2}$, and $\tan \theta = \frac{b}{a}$, $0 \le \theta \lt 2\pi $.
So, for the complex number $z=-3$, we have$$r=\sqrt{(-3)^2+0^2}=\sqrt{9}=3, \\ \cos \theta =\frac{a}{r}=\frac{-3}{3}=-1.$$ So$$\theta =\pi $$Thus, the complex number has the polar form$$z=3 \left ( \cos \pi +i \sin \pi \right ).$$
